14 comments:

Fun problem, especially since I'm relearning my calculus and am looking for reasons to use it. I got 64 / 15\pi, but did so much calculation along the way that I assume 1) I did something wrong somewhere and 2) there must be a simpler way to do it. At least the size of the answer is plausible.

Maybe I'm slow, but I don't get what "average" means in this case. How are the different "rings" weighted? If a particular line of latitude has twice the circumference of another, does it have twice as many infinite points from the given points? The same number?